Aspects of 2-algebras: operads, bimodules and analytic functors

André Joyal
Université du Québec à Montréal (UQAM)
https://professeurs.uqam.ca/professeur/joyal.andre/

Date(s) : 06/10/2016   iCal
11 h 00 min - 12 h 00 min

We exploit the analogy between the notion of symmetric monoidal closed category and that of commutative ring. We say that a presentable monoidal closed category is a 2-rig (a rig is like a ring, but the addition may not have an inverse). A category enriched over a 2-rig is like a module over a ring. The 2-category of symmetric 2-rigs is similar to the category of commutative rings. Polynomial functors are like polynomial functions. The category of polynomial functors is cartesian closed (by a result of Hyland Fiore, Gambino, Winskel). We extend this result to the category of bimodules between operads.

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